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The normal curvature approach model is a new method proposed for generating interference-free tool paths in machining the freeform surfaces on five-axis CNC machines, and a specialized whirlwind milling tool is also introduced in the paper. The crux of this new tool path model is to optimize the CL-data of whirlwind milling tool so as to closely approach to the surface being machined. So, this new milling method evidently raises the material removal rate at the point of contact. The stepforwards and step-overs of NC tool paths are determined by the accuracy of the manufactured surfaces. Under the same scallop height and dimensional precision, this method can shorten the number of tool passes and cut down the manufacturing cost.